This invention relates to an apparatus for controlling the control angle for AC-DC thyristor converters in a DC power transmission system while maintaining the damping losses of damping circuits in the converters to less than a predetermined limit, and more particularly to a DC power transmission control apparatus which is capable of exhibiting a maximum control function for the contro. of the reactive power.
Briefly describing, a DC power transmission system is a means for interconnecting two AC systems by a DC power transmission line and comprises AC-DC converters for the mutual conversion between the AC power and the DC power. In the DC power transmission system, one of the thyristor converters operates as a forward converter or a rectifier, while the other operates as a reverse converter or an inverter, and for example, the rectifier is placed under constant current control, while the inverter is placed under constant voltage control or constant extinction angle control so as to permit interchange of power between the two AC systems.
When looked from the side of the electric generator in any one of the AC systems, the AC-DC converter is a load with a retarded power factor which is adjustable. Thus, the AC-DC converter can also serve the function of controlling the reactive power in the AC system in addition to the power conversion function above described. Especially, when the electric generator is connected to a large-capacity cable system, a super-high voltage transmission system or a long-distance power transmission line, the operation of the generator with an advanced phase becomes a matter of consideration in a light loaded condition, but this problem can be obviated by the reactive power control function of the converter.
This reactive power control function will be explained in more detail. Now, the active power and reactive power in the output of the generator connected to the load are designated by P.sub.g and Q.sub.g, those of the converters are designated by P.sub.i and Q.sub.i, and those of the load are designated by P.sub.l and Q.sub.l, respectively. Then, in the AC system connected to the reverse converter or inverter, the relations P.sub.g =P.sub.l -P.sub.i and Q.sub.g =Q.sub.i +Q.sub.l hold. Suppose then that the active power P.sub.l of the load is constant, and the retarded(delay)-phase reactive power load Q.sub.L decreases. In such a case, the generator is inevitably placed in an advance phase operation. Such as operation of the generator can be avoided by detecting the power factor of the generator and increasing the control angle .beta. for the reverse converter so as to increase the consumption of the reactive power Q.sub.i. The above description has referred to the effectiveness of the reactive power control by the converter for the purpose of avoiding the advance phase operation of the generator. This is also effective in controlling the voltage in the AC system to be constant. For example, by increasing the reactive power consumed by the converter connected to the AC system operating with an advanced power factor, the AC voltage at the AC-DC connection point decreases, while by decreasing the reactive power consumed by the converter, the AC voltage at the connection point increases. The above fact can be utilized for the AC voltage control. Further, the above manner of reactive power control in the AC system by the converter is advantageous in that the reactive power can be controlled at a high speed. From the viewpoint of utilizing the converter for the above purpose, it can be said that the larger the reactive power controlled by the converter, the greater is the rate of contribution to the improvement in the stability of the AC system.
The reactive power consumed by the converter is approximately expressed by the following equation (1): ##EQU1## where Q: reactive power
e.sub.2 : AC voltage at AC terminal of converter PA1 I.sub.d : DC current at DC terminal of converter PA1 .pi.: ratio of circumference of circle to its diameter PA1 .alpha.: control delay angle PA1 .beta.: control advance angle PA1 u: commutation angle PA1 .gamma.=.beta.-u: extinction angle
In the equation (1), .phi. is given as follows: ##EQU2## where .phi.: power factor angle (phase difference between AC current and AC voltage)
The value of Q obtained by introducing the value of .phi. given by the equation (2) into the equation (1) provides the reactive power consumed by the forward converter, and the value of Q obtained by introducing the value of .phi. given by the equation (3) into the equation (1) provides the reactive power consumed by the reverse converter. It will be apparent from the equations (1), (2) and (3), the larger the control delay angle .alpha. or the control advance angle .beta., the greater is the reactive power consumed by the converter, provided that the AC voltage e.sub.2 and DC current I.sub.d are constant, and .phi.&lt;.pi./2 radians.
However, even when the value of .phi. lies within the range of .phi.&lt;.pi./2 radians, there is a limit in the increase of the control angles .alpha. and .beta. for the purpose of control of the reactive power. The reasons will be described presently. The thyristor converter comprises a plurality of thyristors connected in series to constitute a plurality of groups, and a series circuit of a resistor R and a capacitor C, or a so-called damping circuit, is connected across the anode and the cathode of each thyristor or each thyristor group so as to prevent potential fluctuation and other troubles during commutation of the thyristors. In this circuit, there occurs normally a loss given approximately by (R.multidot.I.sub.d 2+1/2C e.sub.2 2), and this loss increases with the increase in the control angles .alpha. and .beta.. Therefore, with the increase in the control angles .alpha. and .beta., the efficiency of conversion is reduced, and the heat generated from the thyristor valves becomes excessive until finally it is not negligible. Further, when it is desired to operate the converter continuously within the control angle range in which .alpha. and .beta. have large values, the resistors R and capacitors C having the capacities enough to compensate the damping losses of the damping circuits are required, and the proportion of the space occupied by the damping circuits in the thyristor values increases considerably, resulting in a bulky converter which is undesirable. The relation between the control angles of the damping loss of the converter is disclosed in, for example, a paper entitled "Calculation of Damper Losses in HVDC Converters" IEEE Summer Power Meeting, Dalla, Texas, June 22-27, 1969.
As described hereinbefore, the positive utilization of AC-DC thyristor converters for the reactive power control provides a remarkable merit in view of their dual control functions. However, in the present status of the reactive power control, the damping loss in the thyristor valves is not entirely taken into account although the above problem is encountered in the effort of increasing the reactive power consumed by the converter. The neglect of the above problem in the present status of the reactive power control gives rise to various problems including an undesirable reduction in the conversion efficiency of the converter and an undesirable generation of excessive heat from the thyristor valves. Further, due to the fact that the present status is as described above, no efforts have so far been made to attain the desired reactive power control by fully exhibiting the reactive power control function of the converter within the control angle range which will not increase the damping loss.
While the above description has referred to the problems encountered in the reactive power control when the control angles are maintained at large values for an extended period of time of operation by way of example, such problems may occur also during operation at a low load, resulting also in an undesirable reduction in the efficiency of conversion.